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Bob has a not even coin, every time he tosses the coin, the probability that the coin's front face up isqp(qp≤12)\frac{q}{p}(\frac{q}{p} \le \frac{1}{2})​p​​q​​(​p​​q​​≤​2​​1​​).The question is, w

f(cos(x))=cos(n∗x) holds for all xxx.Given two integers nnn and mmm, you need to calculate the coefficient of xmx^mx​m​​ in f(x)f(x)f(x), modulo 998244353998244353998244353.Input Format

Define the function S(x)S(x)S(x) for xxx is a positive integer. S(x)S(x)S(x) equals to the sum of all digit of the decimal expression of xxx. Please find a positive integer kkk that S(k∗x)